Week 2 Geometric Series

Week 2: This week in Pre Calculus 11 we learned about infinite and finite geometric series.

GEOMETRIC SEQUENCES – Each term is multiplied by a constant, known as the common ratio.

There are two types of infinite geometric series. (adding the sequence is a series to find a sum).

DIVERGING – A diverging series means the ratio is r > 1 or r < -1. This means the number of terms will increase, which means the partial sum increases, so the series does not have a finite sum. (NO SUM) It only has a sum if it is asking for a specific sum of terms.

CONVERGING – A converging series means the ratio is 1 > r > 0 (smaller than 1, bigger than 0) or -1 < r < 0. ( bigger that -1, smaller than 0). The partial sum will appear to get closer to a number, therefore we estimate the finite sum. (HAS SUM).

To find the sum:

Find Ratio

Identify if it Diverges or Converges.

Diverges, STOP (No Sum)

Converges, CONTINUE (Sum)

Use the formula

ex. 8 + 16 + 32 + 64 + 128 + 256 …

Ratio:

Identify: Diverges. NO SUM

ex. 2) 8 + -7.2 + 6.48 + -5.832 + 5.2488 …

Ratio:

Identify: Converges, ratio is a decimal bigger that -1 but smaller than 0.